Question: William is 12 years older than Nadia. Sixteen years ago, William was 3 times as old as Nadia. How old is Nadia now?
Solution: We can use the given information to write down two equations that describe the ages of William and Nadia. Let William's current age be $w$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $w = n + 12$ Sixteen years ago, William was $w - 16$ years old, and Nadia was $n - 16$ years old. The information in the second sentence can be expressed in the following equation: $w - 16 = 3(n - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = n + 12$ . Substituting this into our second equation, we get the equation: $(n + 12)$ $-$ $16 = 3(n - 16)$ which combines the information about $n$ from both of our original equations. Simplifying both sides of this equation, we get: $n - 4 = 3 n - 48$ Solving for $n$ , we get: $2 n = 44$ $n = 22$.